Some Newman Contractible Manifolds with Disjoint Spines
by
Bud Sanders
University of Tennessee

A compact polyhedron K in the interior of a PL manifold M is said to be a spine of M if M collapses to K. The manifold M has disjoint spines provided that it collapses (independently) to two disjoint polyhedra in its interior. The question arises as to which contractible manifolds have a pair of disjoint spines. A technique of M.H.A. Newman provides contractible manifolds which are not balls. A Newman manifold is constructed as the closure of the complement of a regular neighborhood of a finite, acyclic, simplicial complex K in Sⁿ with \pi₁(K) =/= { 1 } for large enough n. It is denoted New(K, n). Craig Guilbault has shown that if K is any finite, non-simply connected, acyclic k-complex then New(K, n) has disjoint spines provided n > 4k. If K is a non-simply connected, acyclic 2-complex, it will be shown that New(K, n) has disjoint spines when n > 6.

Date received: February 6, 1998